I don't agree - an IDE is completely different to either a library or a framework; it provides you with an environment in which you can write/debug/test your implementation of either.

A SDK might be a bit of both worlds here - "here's a collection of libraries for you to use while working on $project, and you should use our Framework/API to structure how you do it" - but it's not imnsho a framework per se.

I keep coming back to:

an API or Framework is a (more or less) abstract definition of exposed surfaces between components.